Not at all! Black can only mean black. It may not be a colour in scientific terms, but if you're talking about hair - it's a specific colour. 'Dark' simply means 'not light'. This, of course, is relative. In countries where many people have light-coloured and blond hair, anything darker than light brown might be described as 'dark'. Just as an example, take a look at Elena's profile picture. In a country such as Finland, for instance, someone with her nice chestnut-brown hair colour might be considered as 'dark-haired' in comparison with the colouring of the predominantly fair-haired native population.

Dark hair might mean brown, or hair that used to be black /brown and now is grey.

There is a wide range of hair color in North America and Northern Europe and, black is relatively rare, unlike in Southern Europe and Asia. As Su. Ki. mentioned, anything darker than average will be called dark hair if a more precise colour is not mentioned.

Of course they are different. Dark can be dark brown but not black.